analgesic vs painkiller

analgesic and painkiller both are nouns.

Word	Noun	Adjective	Verb	Adverb
analgesic	Yes	Yes	No	No
painkiller	Yes	No	No	No

As nouns, analgesic and painkiller are synonyms defined as:

Other synonyms of analgesic include anodyne, pain pill.

analgesic (noun)	painkiller (noun)
a medicine used to relieve pain	a medicine used to relieve pain

analgesic (adjective)	painkiller (adjective)
capable of relieving pain